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1 Introduction/ n6 [9 C" e. {2 h
1.1 Photonics: the countless possibilities of light propagation: K. |% S9 @- q* O9 @
1.2 Modelling photonics0 U; y+ f2 j6 a
2 Full-vectorial Beam Propagation Method
+ R- Q! j/ I5 M8 M/ r2.1 Introduction) @0 j5 ~9 G- p1 ]3 e- t/ x) o
2.2 Overview of the beam propagation methods
& ]/ J: ?" j1 \# x8 l/ @$ l2.3 Maxwell’s Equations
7 z$ B4 A- d6 h" l1 @2.4 Magnetic field formulation of the wave equation
$ w G: w- ]. D, C8 J: M/ [2.5 Electric field formulation of the wave equation/ t' {$ S% q& q
2.6 PeRFectly-Matched Layer% C9 b. Z8 P' D3 z; t
2.7 Finite Element Analysis
# X7 O, N( }1 k- s! t2.8 Derivation of BPM Equations% s3 \! p" T* z" t+ |$ @# R2 F5 ^
2.9 Imaginary-Distance BPM: Mode Solver
( o" [8 ?+ J+ v( C3 Assessment of Full-Vectorial Beam Propagation Method4 m0 m! B; |9 d2 H% n
3.1 Introduction
7 }( h3 t- i! w2 r3.2 Analysis of Rectangular waveguide
% I1 b7 w d) ~: G2 K3.3 Photonic Crystal Fibre1 H- t2 B! {9 e6 Y* s9 I
3.4 Liquid Crystal Based Photonic Crystal Fibre" h. {9 v0 C3 ], M
3.5 Electro-optical Modulators
% o9 U! P. w- v9 G: v3.6 Switches
# ]7 g3 Q% f5 c4 Bidirectional Beam Propagation Method
8 _# X4 q! p" u f; }. k: ^ o$ g6 Y7 o4.1 Introduction$ W: `" U4 E& z; q* A" @
4.2 Optical Waveguide Discontinuity Problem
# c. @" D8 @. U, t7 w; i4.3 Finite element analysis of discontinuity problems! X, V+ C" W% @) U# n8 r7 e
4.4 Derivation of Finite Element Matrices1 T. \. b1 {0 h: z# I7 X6 t0 r; A5 z: _
4.5 Application of Taylor’s Series Expansion7 ^0 Q: L2 ~1 t+ a# A
4.6 Computation of Reflected, Transmitted and Radiation Waves
5 Y: ^$ U& ?4 g, w4 \3 m7 {4.7 Optical fiber-facet problem/ |8 @* B/ y. c+ l9 P
4.8 Finite element analysis of optical fiber facets4 V# B3 m0 M' |* ?* z* F4 z# _3 W
4.9 Iterative analysis of multiple-discontinuities
: L4 z# m1 F+ h/ Y/ j. k, E5 J4.10 Numerical assessment
' h4 u$ ? H9 ~* Z: \/ s( C5 Complex-Envelope Alternating-Direction-Implicit Finite Difference Time Domain Method with Assessment
! _% C3 v% I' L0 X5.1 Introduction
# S+ G( E; m' u- O2 x4 \ d5.2 Maxwell's equations) m# _( K0 y' v! d6 o
5.3 Brief history of Finite Difference Time Domain (FDTD) Method' w9 g* @2 r* H; v$ h; F9 E' F4 N
5.4 Finite Difference Time Domain (FDTD) Method
; E+ X/ u) x2 A# L5.5 -Direction-Implicit FDTD (ADI-FDTD): Beyond the Courant Limit9 a" E3 y8 l: x' i
5.6 Complex-Envelope ADI-FDTD (CE-ADI-
" ^* d+ G% n& I& ^5 x5.7 Perfectly Matched Layer (PML) Boundary Conditions8 _$ M7 {7 N4 `: R1 i; |) _
5.8 Uniaxal Perfectly Matched Layer (UPML) Absorbing Boundary Condition" M2 O- O) w h0 j: s
5.9 PML Parameters3 Z3 n( E; U+ k# m* a% Y" j
5.10 PML Boundary Conditions for CE-ADI-FDTD
4 O4 R/ E& K5 [- M5.11 PhC Resonant Cavities3 @+ P- Z5 F# W& o/ p$ ?4 g
5.12 5x5 Rectangular Lattice PhC Cavity
; p7 }- }2 e4 I9 Z5.13 Triangular Lattice PhC Cavity
2 V& m' f8 P, w5.14 Wavelength Division Multiplexing
9 E9 v4 M6 j% G: u' z5.15 Conclusions
* [* g6 l! S' ?1 ~9 v; W( f7 A6. Finite Volume time Domain (FVTD) Method' D$ O6 w V2 {
6.1 Introduction7 G# i' K7 b+ r+ G# \* P3 B1 |
6.2 Numerical analysis7 V0 \1 o# u4 O& j9 v% ~
6.3 UPWIND Scheme for the Calculation0 I9 V) i" V# R4 L" i1 T. P
6.4 NON-DIFFUSIVE Scheme for the Flux Calculation
* M# ^9 \( \" V; u6.5 2D Formulation of the FVTD Method& H! i, j- X' I6 a
6.6 Boundary Conditions
& @ x' [5 Y- i" ]/ d3 G6.7 Nonlinear Optics
4 V" n: q' g1 C& l6.8 Nonlinear Optical Interactions2 L8 M" v9 P9 |4 m
6.9 Extension of the FDTD Method to Nonlinear Problems
5 Z! Z' J7 e, F0 t6.10 Extension of the FVTD Method to Nonlinear Problems. m) ]" w7 V( P
6.11 Conclusions
+ M2 R) c7 b# g% V7 Numerical Analysis of Linear and Nonlinear PhC Based Devices0 T4 y! \1 Q( f1 q5 l _
7.1 Introduction
$ _8 V9 ?( m) M/ @- p7.2 FVTD Method Assessment: PhC Cavity
7 E K; t" X) ~- D7.3 FVTD Method Assessment: PhC Waveguide
& d' W! u/ |+ X7.4 FVTD Method Assessment: PBG T-Branch
, |8 j, n. {+ r5 g3 ^7.5 PhC Multimode Resonant Cavity
0 y$ u' ^. Q. c3 I7.6 FDTD Analysis of Nonlinear Devices+ x# X$ ~0 f# M2 C$ y0 o6 `
7.7 FVTD Analysis of Nonlinear Photonic Crystal Wires
: X# ]3 I/ _2 G; M7.8 Conclusions$ F8 A- q7 m8 h' B
8 Multiresolution Time Domain+ l. N) W! _; `5 C r z' e
8.1 Introduction
- P+ Y1 a0 i' s D9 V8.2 MRTD basics
' Z# i# Q! k( c) _$ [$ D8 g8.3 MRTD update scheme
' H5 R* y, s/ p/ _8 Z8.4 Scaling-MRTD
5 b k* I; ~+ s6 O8.5 Conclusions
m9 H6 r- @- \) q/ q0 e& W Y9 MRTD Analysis of PhC-Devices m+ ~6 ?/ s s; H3 W! w0 R
9.1 Introduction5 k: X9 s8 r5 i9 a3 y% V9 ?$ S
9.2 UPML-MRTD: test and code validation* J% ]' P8 o ^( h. h6 ]' ], z
9.3 MRTD vs FDTD for the analysis of linear photonic crystals, ?8 R$ }0 V. w
9.4 Conclusions
6 P5 b4 j- W6 r% k4 Q7 ]10 MRTD Analysis of SHG PhC-Devices0 p( q4 ^# C9 a0 v5 D7 {; @: B
10.1 Introduction7 w1 _( ^( V/ t$ W0 z
10.2 Second hARMonic generation in optics5 k9 v0 J8 J0 r# T) {0 Y6 q* P& Y
10.3 Extended S-MRTD for SHG analysis
, ^' D9 i. [; U1 D3 Z. E10.4 SHG in PhC-waveguide6 p1 \1 e' S% W9 {+ h
10.5 Selective SHG in compound PhC-based structures$ a J" F) @3 l( G' j0 y
10.6 New design for selective SHG: PhC-microcavities coupling- L) H9 [9 Y3 K' o* [% j B
10.7 Conclusions
) I) P( O( k0 G! C7 {! E11 Dispersive Nonlinear MRTD for SHG Applications6 r, B; u0 G; j+ ?& I. p9 V
11.1 Introduction
* s. b8 o3 b3 W- M9 D11.2 Dispersion analysis
. ^8 u3 `) p/ J. K11.3 SHG-MRTD scheme for dispersive materials
" R* n& x8 x/ k5 o+ X11.4 Simulation results
$ \1 ^5 G) I7 N4 c11.5 Conclusions |
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